`A B C D` is a quadrilateral; `P , Q , Ra n dS` are the points of trisection of side AB ,BC ,CD and DA respectively and are adjacent to A and C ; prove that `P Q R S` is parallelogram.

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

P, Q , R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,D A respectively. Prove that P Q R S is a rectangle.

D, E and F are the mid-points of the sides AB, BC and CA respectively of A ABC. AE meets DF at O. P and Q are the mid-points of OB and OC respectively. Prove that DPOF is a parallelogram.

P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC=BD and ACbotBD . Prove that PQRS is a square.

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PB = QC

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.